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SUMMARY:Essential Expansion is Forceable - Gabor Kun (Rényi Institute)
DTSTART:20161116T143000Z
DTEND:20161116T153000Z
UID:TALK68664@talks.cam.ac.uk
CONTACT:Andrew Thomason
DESCRIPTION:We say that a sequence of bounded degree graphs is locally\n(B
 enjamini-Schramm) convergent if for every r the probability distribution o
 n the isomorphism classes of rooted r-balls obtained by picking a vertex x
  uniformly at random and considering the r-ball centred at x converges in 
 distribution. Not much is known about approximation of large graphs by sma
 ll ones. We do not even know if every Cayley graph can be approximated by\
 nfinite graphs: This is the famous problem if every group is sofic.\n\nWe 
 prove Bowen's conjecture that for every group G with Kazhdan Property (T) 
 if a sequence of bounded degree graphs locally converges to a Cayley graph
  of G then\nthe sequence is essentially a vertex-disjoint union of expande
 r graphs. We characterize such sequences in terms of the Markov operator.\
 n
LOCATION:MR5
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